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CPS2099 Takatsugu Yoshioka et al.

















                   where ,  =  +  ,  =  +  , and ‘*’ indicates missing data. We partition
                                     2
                                1
                                                 2
                                            1
                 (1)  into a  × 1 random vector and a random vector as   (1)  = (  (1) ′ ,  (1) ′ )′ ,
                          1
                                                                                2
               where  = 1,2, … ,   . We define the sample mean vectors as
                                 1





                   and the sample covariance matrices are given as










                   We consider the following hypothesis test problem:


                   where  is a specified vector. We can construct the Hotelling’s T2 type test
                          0
               statistic as


                   Where















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